Journal d’Analyse Mathématique

, Volume 34, Issue 1, pp 86–119

Regularity in elliptic free boundary problems I

  • D. Kinderlehrer
  • L. Nirenberg
  • J. Spruck
Article

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References

  1. 1.
    S. Agmon, A. Douglis and L. Nirenberg,Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, II, Comm. Pure Appl. Math.12 (1959), 623–727;17 (1964), 35–92.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    N. Aronszajn,A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl.36 (1957), 235–249.MathSciNetMATHGoogle Scholar
  3. 3.
    H. Brézis and D. Kinderlehrer,The smoothness of solutions of nonlinear variational inequalities, Indiana Univ. Math. J.23 (1973), 831–844.CrossRefMathSciNetGoogle Scholar
  4. 4.
    L. A. Caffarelli,The regularity of free boundaries in higher dimensions, Acta Math.139 (1977), 155–184.CrossRefMathSciNetGoogle Scholar
  5. 5.
    P. Garabedian and M. Schiffer,Variational problems in the theory of elliptic partial differential equations, J. Rat. Mech. Anal.2 (1953), 137–171.MathSciNetGoogle Scholar
  6. 6.
    D. Kinderlehrer,Variational inequalities and free boundary problems, Bull. Amer. Math. Soc.84 (1978), 7–26.MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    D. Kinderlehrer and L. Nirenberg,Regularity in free boundary value problems, Ann. Scuola Norm. Sup. Pisa, Ser. IV,4 (1977), 373–391.MATHMathSciNetGoogle Scholar
  8. 8.
    D. Kinderlehrer, L. Nirenberg and J. Spruck,Regularité dans les problèmes elliptiques à frontière libre, to appear in C. R. Acad. Sci.Google Scholar
  9. 9.
    D. Kinderlehrer and J. Spruck,The shape and smoothness of stable plasma configurations, Ann. Scuola Norm. Sup. Pisa. Ser. IV,5 (1978), 131–148.MATHMathSciNetGoogle Scholar
  10. 10.
    H. Lewy,On the reflection laws of second order differential equations in two independent variables, Bull. Amer. Math. Soc.65 (1959), 37–58.MATHMathSciNetGoogle Scholar
  11. 11.
    C. B. Morrey, Jr.,Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York-Berlin, 1966.MATHGoogle Scholar
  12. 12.
    J. C. C. Nitsche,The higher regularity of liquid edges in aggregates of minimal surfaces, Nachr. Akad. Wiss. Göttingen Math.-Phys Kl. II, (1977), 75–95.Google Scholar
  13. 13.
    J. Taylor,The stucture of singularities in soap-bubble-like and soap-film-like minimal surfaces, Ann. of Math.103 (1976), 489–539.CrossRefMathSciNetGoogle Scholar
  14. 14.
    G. Vergara-Caffarelli,Regolarità di un Problema di Disequazioni Relativo a Due Membrane, Rend. Acad. Lincei50 (1971), 659–662.MATHMathSciNetGoogle Scholar

Copyright information

© The Weizmann Science Press of Israel 1978

Authors and Affiliations

  • D. Kinderlehrer
    • 1
    • 2
  • L. Nirenberg
    • 1
    • 2
  • J. Spruck
    • 1
    • 2
  1. 1.University of MinnesotaMinneapolisUSA
  2. 2.Courant InstituteNew York UniversityNew YorkUSA

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